:Using the notion of the radical of an ideal, the conclusion says that " f " belongs to the radical of " I ".
2.
The notion of a Goldman ideal can be used to give a slightly sharpened characterization of a radical of an ideal : the radical of an ideal " I " is the intersection of all Goldman ideals containing " I ".
3.
The notion of a Goldman ideal can be used to give a slightly sharpened characterization of a radical of an ideal : the radical of an ideal " I " is the intersection of all Goldman ideals containing " I ".
4.
For example, it can readily compute Gr�bner basis, syzygies and minimal free resolution, intersection, division, the radical of an ideal, the ideal of zero-dimensional schemes, Poincare series and Hilbert functions, factorization of polynomials, toric ideals.
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